![Open Access](https://i-scholar.in/lib/pkp/templates/images/icons/fulltextgreen.png)
![Restricted Access](https://i-scholar.in/lib/pkp/templates/images/icons/fulltextred.png)
Crust and Skeleton Approximation from Samples
Samples of shape boundary carry the information of the shape for a sufficiently dense sampling. There is not any connectivity information between sample points and the geometry or topology of the original shape is not known. These samples are used for crust and skeleton approximation. In this article, we focus on the Voronoi-based methods which the shape is defined by a set of sample points on the shape boundary and then the shape and its skeleton is approximated with the Voronoi diagram of these points. These methods are extremely sensitive to noise and boundary perturbation. To overcome the problems of crust and skeleton extraction, we propose a new method by labeling the sample points. The conceptual structure and the results illustrate that our method are stable, easy to implement, robust and able to handle sharp corners and open curves, even in the presence of significant noise and perturbations.
Keywords
Sample Points, Crust, Skeleton, Voronoi Diagram, Delaunay Triangulation
User
Information
- Amenta, N., Bern, M. W., & Eppstein, D. (1998). The crust and the beta-skeleton: combinatorial curve reconstruction. Graphical models and image processing. 60(2), 125–135.
- Blum et al., H. (1967). A transformation for extracting new descriptors of shape. Models for the perception of speech and visual form. 19(5), 362–380.
- Blum, H., & Nagel, R. N. (1978). Shape description using weighted symmetric axis features. Pattern Recognition. 10(3), 167–180.
- Bookstein FL (1979) The line-skeleton. Computer Graphics & Image Processing. 11(2), 123–137.
- Giesen, J., Miklos, B., & Pauly, M. (2007). Medial axis approximation of planar shapes from union of balls: A simpler and more robust algorithm. Paper presented at the Proc. Canad. Conf. Comput. Geom, 105-108.
- Gold, C. (1999). Crust and anti-crust: a one-step boundary and skeleton extraction algorithm. Paper presented at the Proceedings of the fifteenth annual symposium on Computational geometry, 189-196.
- Gold, C., & Dakowicz, M. (2005). The Crust and Skeleton–Applications in GIS. Paper presented at the Proceedings, 2nd. Int. Sym. on Voronoi Diagrams in Sci. & Eng. 33-42.
- Gold, C., & Snoeyink, J. (2001). A one-step crust and skeleton extraction algorithm. Algorithmica, 30(2), 144–163.
- Karimipour F, Delavar MR and Frank AU (2010) A Simplex-Based Approach to Implement Dimension Independent Spatial Analyses. J.Computer & Geosci. 36(9), 1123-1134.
- Ledoux, H. (2006). Modelling Three-dimensional Fields in Geo-Science with the Voronoi Diagram and its Dual. Ph.D., School of Computing, University of Glamorgan, Pontypridd, Wales, UK.
![](https://i-scholar.in/public/site/images/abstractview.png)
Abstract Views: 611
![](https://i-scholar.in/public/site/images/pdfview.png)
PDF Views: 106